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XXI.—On the Dominance Ratio

Published online by Cambridge University Press:  15 September 2014

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Summary

The frequency ratio of the allelomorphs of a Mendelian factor is only stable if selection favours the heterozygote: such factors, though occurring rarely, will accumulate in the stock, while those of opposite tendency will be eliminated.

The survival of a mutant gene although established in a mature and potent individual is to a very large extent a matter of chance ; only when a large number of individuals have become affected does selection, dependent on its contribution to the fitness of the organism, become of importance. This is so even for dominant mutants; for recessive mutants selection remains very small so long as the mutant form is an inconsiderable fraction of the interbreeding group.

The distribution of the frequency ratio for different factors may be calculated from the condition that this distribution is stable, as is that of velocities in the Theory of Gases : in the absence of selection the distribution of log is given in fig. 1. Fig. 2 represents the case of steady decay in variance by the action of random survival (the Hagedoorn effect).

Fig. 3 shows the distribution in the somewhat artificial case of uniform genetic selection : this would be the distribution to be expected in the absence of dominance. Fig. 4 shows the asymmetrical distribution due to uniform genotypic selection with or without homogamy.

Under genotypic selection the dominance ratio for complete dominance comes to be exactly ⅓, in close agreement with the value obtained from human measurements.

The rate of mutation necessary to maintain the variance of the species may be calculated from these distributions. Very infrequent mutation will serve to counterbalance the effect of random survival; for equilibrium with selective action a much higher level is needed, though still mutation may be individually rare, especially in large populations.

It would seem that the supposition of genotypic selection balanced by occasional mutations fitted the facts deduced from the correlations of relatives in mankind.

Type
Proceedings
Copyright
Copyright © Royal Society of Edinburgh 1923

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References

REFERENCES

(1)Darwin, Charles, The Origin of Species.Google Scholar
(2)East, E. A., and Jones, D. F., Inbreeding and Outbreeding (1920).Google Scholar
(3)Fisher, R. A., “The Correlation between Relatives on the Supposition of Mendelian Inheritance,” Trans. Royal Soc. Edin., 1918, lii, pp. 399433.Google Scholar
(4)Hagedoorn, A. L. and A. C., , The Relative Value of the Processes causing Evolution (The Hague: Martinus Nijhoff), p. 294 (1921).Google Scholar
(5)Jennings, H. S., “Numerical Results of Diverse Systems of Breeding,” Genetics, i, 5389 (1916).Google Scholar
Jennings, H. S., “The Numerical Results of Diverse Systems of Breeding with respect to two pairs of characters, linked or independent; with special relation to the effects of linkage,” Genetics, ii, 97154 (1917).Google Scholar
(6)Pearson, K., “On a Generalised Theory of Alternative Inheritance, with special reference to Mendel's Laws,” Phil. Trans., cciii, A, pp. 5387 (1903).Google Scholar
(7)Muller, H. J., “Genetic Variability: twin hybrids arid constant hybrids in a case of balanced lethal factors,” Genetics, iii, 422499 (1918).Google Scholar
(8)Robbins, R. B., “Some Applications of Mathematics to Breeding Problems,” Genetics, ii, 489504 (1917).CrossRefGoogle Scholar
Robbins, R. B., “Applications of Mathematics to Breeding Problems, II,” Genetics, iii, 7392 (1918).CrossRefGoogle Scholar
Robbins, R. B., “Some Applications of Mathematics to Breeding Problems, III,” Genetics, iii, 375–306 (1918).CrossRefGoogle Scholar
(9)Wentworth, E. N., and Remick, B. L., “Some Breeding Properties of the Generalised Mendelian Population,” Genetics, i, 608616 (1916).Google Scholar
(10)Wright, S., “Systems of Mating,” Genetics, vi, 111178 (1921).CrossRefGoogle Scholar